Time and Econometrics•Time Series elements of cross-sectional (Retrospective designs)•Univariate Time Series Models•Multivariate Static Models •Multivariate Dynamic Models –Stationary Variables–Non-Stationary Variables•Panel Econometrics •Note: Most of the methods we examine are single-equation methods so bear in mind potential extensions in to multi-equation methods

Some Time Series/Stochastic Processes•Fertility in America•Vote Share of the Democrats in the 20thCentury•Ice-cream Consumption •Barium Chloride Imports in to the US•Capital Expenditures and Appropriations

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Introduction•Economists are often interested in variables that change across time rather than across individuals.•Simple Static models relate a time series variable to other time series variables.•The effect is assumed to operate within the period.

Dynamic Models•Dynamic effects.–Policy takes time to have an effect.–The size and nature of the effect can vary over time.–Permanent vs. Temporary effects.

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•Macroeconomics–e.g. the effect of M on Y in short run vs. the long run•this is know as impulse response function–money supply increases by 1 in year 1–returns to normal afterwards –what happens to y over timetimeY

Distributed Lag•Effect is distributed through time–consumption function: effect of income through time–effect of income taxes on GDP happens with a lag–effect of monetary policy on output through timeyt= α+ β0xt+ β1xt-1+ β2xt-2+ etittixyE-=δδβ)(

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Two Questions1. How far back? - What is the length of the lag?- finite or infinite2. Should the coefficients be restricted?- e.g. smooth adjustment- let the data decide

Unrestricted Finite DL•Finite: change in variable has an effect on another only for a fixed period–e.g. Monetary policy affects GDP for 18 months –the interval is assumed known with certainty•Unrestricted (unstructured)–the effect in period t+1 is not related to the effect in period t

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